IDEAS home Printed from https://ideas.repec.org/p/ems/eureir/7889.html
   My bibliography  Save this paper

Nonlinear support vector machines through iterative majorization and I-splines

Author

Listed:
  • Groenen, P.J.F.
  • Bioch, J.C.
  • Nalbantov, G.I.

Abstract

To minimize the primal support vector machine (SVM) problem, we propose to use iterative majorization. To do so, we propose to use it- erative majorization. To allow for nonlinearity of the predictors, we use (non)monotone spline transformations. An advantage over the usual ker- nel approach in the dual problem is that the variables can be easily inter- preted. We illustrate this with an example from the literature.

Suggested Citation

  • Groenen, P.J.F. & Bioch, J.C. & Nalbantov, G.I., 2006. "Nonlinear support vector machines through iterative majorization and I-splines," Econometric Institute Research Papers EI 2006-25, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  • Handle: RePEc:ems:eureir:7889
    as

    Download full text from publisher

    File URL: https://repub.eur.nl/pub/7889/ei2006-25.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hunter D.R. & Lange K., 2004. "A Tutorial on MM Algorithms," The American Statistician, American Statistical Association, vol. 58, pages 30-37, February.
    2. Kiers, Henk A. L., 2002. "Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems," Computational Statistics & Data Analysis, Elsevier, vol. 41(1), pages 157-170, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Groenen, P.J.F. & Kaymak, U. & van Rosmalen, J.M., 2006. "Fuzzy clustering with Minkowski distance," Econometric Institute Research Papers EI 2006-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Groenen, P.J.F. & Nalbantov, G.I. & Bioch, J.C., 2007. "SVM-Maj: a majorization approach to linear support vector machines with different hinge errors," Econometric Institute Research Papers EI 2007-49, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Rasmus Lentz & Jean Marc Robin & Suphanit Piyapromdee, 2018. "On Worker and Firm Heterogeneity in Wages and Employment Mobility: Evidence from Danish Register Data," 2018 Meeting Papers 469, Society for Economic Dynamics.
    4. Markovsky, Ivan & Niranjan, Mahesan, 2010. "Approximate low-rank factorization with structured factors," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3411-3420, December.
    5. Groenen, P.J.F. & Giaquinto, P. & Kiers, H.A.L., 2003. "Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models," Econometric Institute Research Papers EI 2003-09, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Songfeng Zheng, 2021. "KLERC: kernel Lagrangian expectile regression calculator," Computational Statistics, Springer, vol. 36(1), pages 283-311, March.
    7. Sakyajit Bhattacharya & Paul McNicholas, 2014. "A LASSO-penalized BIC for mixture model selection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(1), pages 45-61, March.
    8. Nguyen Thai An & Nguyen Mau Nam & Xiaolong Qin, 2020. "Solving k-center problems involving sets based on optimization techniques," Journal of Global Optimization, Springer, vol. 76(1), pages 189-209, January.
    9. Florian Schwendinger & Bettina Grün & Kurt Hornik, 2021. "A comparison of optimization solvers for log binomial regression including conic programming," Computational Statistics, Springer, vol. 36(3), pages 1721-1754, September.
    10. Krijnen, Wim P., 2006. "Convergence of the sequence of parameters generated by alternating least squares algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 481-489, November.
    11. Utkarsh J. Dang & Michael P.B. Gallaugher & Ryan P. Browne & Paul D. McNicholas, 2023. "Model-Based Clustering and Classification Using Mixtures of Multivariate Skewed Power Exponential Distributions," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 145-167, April.
    12. V. Maume-Deschamps & D. Rullière & A. Usseglio-Carleve, 2018. "Spatial Expectile Predictions for Elliptical Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 643-671, June.
    13. Sanjeena Subedi & Drew Neish & Stephen Bak & Zeny Feng, 2020. "Cluster analysis of microbiome data by using mixtures of Dirichlet–multinomial regression models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1163-1187, November.
    14. Lian, Heng & Meng, Jie & Fan, Zengyan, 2015. "Simultaneous estimation of linear conditional quantiles with penalized splines," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 1-21.
    15. van den Burg, G.J.J. & Groenen, P.J.F., 2014. "GenSVM: A Generalized Multiclass Support Vector Machine," Econometric Institute Research Papers EI 2014-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. Lv, Xiao-Guang & Jiang, Le & Liu, Jun, 2016. "Deblurring Poisson noisy images by total variation with overlapping group sparsity," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 132-148.
    17. Rasmus Lentz & Suphanit Piyapromdee & Jean-Marc Robin, 2022. "The Anatomy of Sorting - Evidence from Danish Data," Working Papers hal-03869383, HAL.
    18. Tian, Guo-Liang & Tang, Man-Lai & Liu, Chunling, 2012. "Accelerating the quadratic lower-bound algorithm via optimizing the shrinkage parameter," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 255-265.
    19. Vu, Duy & Aitkin, Murray, 2015. "Variational algorithms for biclustering models," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 12-24.
    20. Gunter Maris & Han Maas, 2012. "Speed-Accuracy Response Models: Scoring Rules based on Response Time and Accuracy," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 615-633, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ems:eureir:7889. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: RePub (email available below). General contact details of provider: https://edirc.repec.org/data/feeurnl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.